{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The Curse of Dimensionality"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "An increase in the number of dimensions of a dataset means that there are more entries in the vector of features that represents each observation in the corresponding Euclidean space. We measure the distance in a vector space using Euclidean distance, also known as L2 norm, which we applied to the vector of linear regression coefficients to train a regularized Ridge Regression model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Euclidean distance between two n-dimensional vectors with Cartesian coordinates p = (p1, p2, ..., pn) and q = (q1, q2, ..., qn) is computed using the familiar formula developed by Pythagoras:\n",
    "$$d(p, q)=\\sqrt{\\sum_{i=1}^n(p_i−q_i)^2}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hence, each new dimension adds a non-negative term to the sum, so that the distance increases with the number of dimensions for distinct vectors. In other words, as the number of features grows for a given number of observations, the feature space becomes increasingly sparse, i.e., less dense or emptier. On the flip side, the lower data density requires more observations to keep the average distance between data points the same."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Imports and Settings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-18T13:35:40.035450Z",
     "start_time": "2020-06-18T13:35:39.574970Z"
    },
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "from numpy import clip, full, fill_diagonal\n",
    "from numpy.random import uniform, multivariate_normal, seed\n",
    "from scipy.spatial.distance import pdist, squareform\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-18T13:35:40.039235Z",
     "start_time": "2020-06-18T13:35:40.036870Z"
    }
   },
   "outputs": [],
   "source": [
    "seed(42)\n",
    "sns.set_style('white')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Simulate pairwise distances of points in $\\mathbb{R}^n$ (while $n$ increases)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The simulation draws features in the range [0, 1] from uncorrelated uniform or correlated normal distributions and gradually increases the number of features to 2,500. \n",
    "\n",
    "The average distance between data points increases to over 11 times the feature range for features drawn from the normal distribution, and to over 20 times in the (extreme) case of uncorrelated uniform distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Compute Distance Metrics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-18T13:35:40.049053Z",
     "start_time": "2020-06-18T13:35:40.040604Z"
    }
   },
   "outputs": [],
   "source": [
    "def get_distance_metrics(points):\n",
    "    \"\"\"Calculate mean of pairwise distances and \n",
    "        mean of min pairwise distances\"\"\"\n",
    "    pairwise_dist = squareform(pdist(points))\n",
    "    fill_diagonal(pairwise_dist, np.nanmean(pairwise_dist, axis=1))\n",
    "    avg_distance = np.mean(np.nanmean(pairwise_dist, axis=1))\n",
    "    fill_diagonal(pairwise_dist, np.nanmax(pairwise_dist, axis=1))\n",
    "    avg_min_distance = np.mean(np.nanmin(pairwise_dist, axis=1))\n",
    "    return avg_distance, avg_min_distance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Simulate Distances"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-18T13:35:40.062044Z",
     "start_time": "2020-06-18T13:35:40.050005Z"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "def simulate_distances(m, n, mean, var, corr):\n",
    "    \"\"\"Draw m random vectors of dimension n \n",
    "        from uniform and normal distributions\n",
    "        and return pairwise distance metrics\"\"\"\n",
    "    uni_dist = get_distance_metrics(uniform(size=(m, n)))\n",
    "    cov = full(shape=(n, n), fill_value=var * corr)\n",
    "    fill_diagonal(cov, var)\n",
    "    normal_points = multivariate_normal(\n",
    "        full(shape=(n,), fill_value=mean), cov, m)\n",
    "    normal_points = clip(normal_points, a_min=0, a_max=1)\n",
    "    norm_dist = get_distance_metrics(normal_points)\n",
    "    return uni_dist, norm_dist"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sampling Parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-18T13:35:40.091233Z",
     "start_time": "2020-06-18T13:35:40.063084Z"
    }
   },
   "outputs": [],
   "source": [
    "n_points = 1000\n",
    "min_dim, max_dim, step = 1, 2502, 100 # from 1 - 2501\n",
    "dimensions = range(min_dim, max_dim, step)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-18T13:33:51.633903Z",
     "start_time": "2020-06-18T13:33:51.631691Z"
    }
   },
   "source": [
    "### Normal Distribution Params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-18T13:35:40.099859Z",
     "start_time": "2020-06-18T13:35:40.092123Z"
    }
   },
   "outputs": [],
   "source": [
    "mean = 0.5 \n",
    "var = (mean/3)**2 # 99% of sample in [0, 1]\n",
    "corr = 0.25"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Run Simulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "col_names = ['Avg. Uniform', 'Min. Uniform', 'Avg. Normal', 'Min. Normal']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-18T13:36:30.950861Z",
     "start_time": "2020-06-18T13:35:40.101289Z"
    },
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "avg_dist = []\n",
    "for dim in dimensions:\n",
    "    uni_dist, norm_dist = simulate_distances(n_points,\n",
    "                                             dim,\n",
    "                                             mean,\n",
    "                                             var,\n",
    "                                             corr)\n",
    "    avg_dist.append([*uni_dist,\n",
    "                     *norm_dist])\n",
    "\n",
    "distances = pd.DataFrame(data=avg_dist,\n",
    "                         columns=col_names,\n",
    "                         index=dimensions)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot Average and Minimum Distance of Points in Unit Hypercube"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-18T13:39:09.530495Z",
     "start_time": "2020-06-18T13:39:08.612788Z"
    },
    "hide_input": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1008x576 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "title = 'Distance of {:,.0f} Data Points in a Unit Hypercube'.format(n_points)\n",
    "fig, axes = plt.subplots(nrows=2, ncols=1, figsize=(14, 8))\n",
    "distances[[ 'Avg. Uniform', 'Avg. Normal']].plot.bar(title='Average ' + title, ax=axes[0], rot=0)\n",
    "distances[[ 'Min. Uniform', 'Min. Normal']].plot.bar(title='Minimum ' + title, ax=axes[1], rot=0)\n",
    "\n",
    "for ax in axes:\n",
    "    ax.grid(axis='y', lw=1, ls='--')\n",
    "    for p in ax.patches:\n",
    "        ax.annotate('{:.1f}'.format(p.get_height()), (p.get_x() + .005, p.get_height() + .25), fontsize=10)\n",
    "    ax.set_ylabel('Distance')\n",
    "\n",
    "axes[1].set_xlabel('Dimensionality')\n",
    "sns.despine()        \n",
    "fig.tight_layout();"
   ]
  }
 ],
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